What are the divisors of 5555?

1, 5, 11, 55, 101, 505, 1111, 5555

There is a total of 8 positive divisors.
The sum of these divisors is 7344.
The arithmetic mean is 918.

8 odd divisors

1, 5, 11, 55, 101, 505, 1111, 5555

How to compute the divisors of 5555?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5555 by each of the numbers from 1 to 5555 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5555 / 1 = 5555 (the remainder is 0, so 1 is a divisor of 5555)
5555 / 2 = 2777.5 (the remainder is 1, so 2 is not a divisor of 5555)
5555 / 3 = 1851.6666666667 (the remainder is 2, so 3 is not a divisor of 5555)
...
5555 / 5554 = 1.0001800504141 (the remainder is 1, so 5554 is not a divisor of 5555)
5555 / 5555 = 1 (the remainder is 0, so 5555 is a divisor of 5555)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5555 (i.e. 74.531872376856). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5555 / 1 = 5555 (the remainder is 0, so 1 and 5555 are divisors of 5555)
5555 / 2 = 2777.5 (the remainder is 1, so 2 is not a divisor of 5555)
5555 / 3 = 1851.6666666667 (the remainder is 2, so 3 is not a divisor of 5555)
...
5555 / 73 = 76.095890410959 (the remainder is 7, so 73 is not a divisor of 5555)
5555 / 74 = 75.067567567568 (the remainder is 5, so 74 is not a divisor of 5555)